16 Jul 2024. Talk by Roberto Rubio at the Poisson Days at Trieste 2024 (SISSA).
Abstract: Complex and symplectic manifolds are, in particular, generalized complex manifolds, a class that supersedes them: there exist neither complex nor symplectic manifolds that are generalized complex. This happens very tightly, as generalized complex manifolds must be almost complex (and hence even dimensional). In this talk, I will show how Bn-generalized geometry, a simple and natural variation of generalized geometry, offers a similar setup for manifolds of any dimension and I will focus on the analogue of generalized complex structures for 3-manifolds and their associated invariants. This is joint work with J. Porti.